Isosceles triangle 9

Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm and altitude is 24cm. Find the area of the isosceles triangle

Correct result:

A =  168 cm²

Solution:

$$\begin{gathered} p=64\text{ cm } \\ h=24\text{ cm } \\ p=2a+b \\ {a}^2=(b\mathrm{/}2{)}^2+h^2 \\ {a}^2=((p-2a)\mathrm{/}2{)}^2+h^2 \\ {a}^2=(p\mathrm{/}2-a{)}^2+h^2 \\ {a}^2=p^2\mathrm{/}4-pa+a^2+h^2 \\ pa=p^2\mathrm{/}4+h^2 \\ a=p\mathrm{/}4+h^2\mathrm{/}p=64\mathrm{/}4+24^2\mathrm{/}64=25\text{ cm } \\ b=p-2\cdot a=64-2\cdot 25=14\text{ cm } \\ {p}_1=2\cdot a+b=2\cdot 25+14=64\text{ cm } \\ {p}_1=p \\ A={\displaystyle \frac{b\cdot h}{2}}={\displaystyle \frac{14\cdot 24}{2}}=168{\text{cm}}^2 \end{gathered}$$

Try calculation via our triangle calculator.

Try another example

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 2 comments:

Steve

No, your solution starts with h=25cm, but the question says that h=24cm.

So, looking at one-half of the isosceles triangle, x² + 24² = (32-x)²    solves to x=7cm,   which gives the area of the isosceles triangle as 7x24 = 168cm²

11 months ago  Like

Dr Math

thank you, we corrected 25 to 24 as altitude....

11 months ago  Like

Next similar math problems:

• Triangle ABC
  In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
• Euclid2
  In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
• RT triangle and height
  Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.
• Catheti
  The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
• Thunderstorm
  The height of the pole before the storm is 10 m. After a storm when they come to check it they see that on the ground from the pole blows part of the column. Distance from the pole is 3 meters. At how high was the pole broken? (In fact, a rectangular tria
• A rectangular patio
  A rectangular patio measures 20 ft by 30 ft. By adding x feet to the width and x feet to the length, the area is doubled. Find the new dimensions of the patio.
• Trapezium
  The lengths of a parallel sides of a trapezium are (2x+3) and (x+8) and the distance between them is (x+4). if the area of the trapezium is 590 , find the value of x.
• Evaluation of expressions
  If a²-3a+1=0, find (i)a²+1/a² (ii) a³+1/a³
• Equation 23
  Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
• Quadratic equation
  Find the roots of the quadratic equation: 3x²-4x + (-4) = 0.
• Solve 3
  Solve quadratic equation: (6n+1) (4n-1) = 3n²
• Equation
  Equation ? has one root x₁ = 8. Determine the coefficient b and the second root x₂.
• Discriminant
  Determine the discriminant of the equation: ?
• Roots
  Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
• Square root 2
  If the square root of 3m² +22 and -x = 0, and x=7, what is m?
• Solve equation
  solve equation: ?
• Roots and coefficient
  In the equation 2x ^ 2 + bx-9 = 0 is one root x1 = -3/2. Determine the second root and the coefficient b.